Thompson made only four starts since Terry Butcher took control of the club in November of last year, with Brown laying the blame squarely at the manager's feet.
"I couldn't see their relegation coming. I don't think anyone could. It's been hard for them and I still can't believe they let Kevin Thomson go," said Brown, according to the Daily Mail.
"Not playing him is the biggest mistake they made. Everyone knows how good a player he is, he went back to the club and played for nothing, got his deal and they were seventh in the league when he was playing week-in, week-out.
"He's not been playing for the last four or five months, and they dropped rapidly down the league. It just shows what one or two players can do, especially with his experience. They would have stayed up 100 per cent if he had played more games."
Hibs will now begin next season in the Scottish Championship.